Journal
INFORMATION SCIENCES
Volume 189, Issue -, Pages 1-17Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ins.2011.11.040
Keywords
Fuzzy multisets; n-Dimensional fuzzy sets; Atanassov operators; OWA operator; n-Dimensional aggregation functions; n-Dimensional negation
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Funding
- Government of Brazil [CNPq 308256/2009-3, CNPq 201118/2010-6]
- Government of Spain [TIN2010-15055, MTM 2009-10962, TIN2009-07901]
- [APVV-0073-10]
- [MSM VZ 6198898701]
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The main aim of this work is to present a generalization of Atanassov's operators to higher dimensions. To do so, we use the concept of fuzzy set, which can be seen as a special kind of fuzzy multiset, to define a generalization of Atanassov's operators for n-dimensional fuzzy values (called n-dimensional intervals). We prove that our generalized Atanassov's operators also generalize OWA operators of any dimension by allowing negative weights. We apply our results to a decision making problem. We also extend the notions of aggregating functions, in particular t-norms, fuzzy negations and automorphism and related notions for n-dimensional framework. (C) 2011 Elsevier Inc. All rights reserved.
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